Here is a lesson in the grammar of financial presentations. Barclays runs a dark pool called Barclays LX. In that dark pool, institutions can trade stocks without publicly displaying their orders, as they would on a stock exchange. Barclays pitched this dark pool to investors by telling them that it monitored the dark pool to keep out "predatory" traders and let in only nice, well-behaved traders. It showed them this chart:

I suppose you could read that chart to mean that LX has a balance of institutional investors (blue circles) and high-frequency traders (green circles), and that they're all nice and well-behaved: There's a lot of green trading (green, in financial presentations, is good), a lot of white trading (white is neutral), and not a lot of pink trading (pink is like red, and red is bad).
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According to New York Attorney General Eric Schneiderman, Barclays wanted its clients to read the chart that way.

The chart did not actually say that, though. You can tell because it starts with the word "Sample." "Sample," in financial presentations, means "not true." In particular, Barclays removed Tradebot, an aggressive high-frequency trading firm, from the chart, because it didn't want the chart to look bad. And then this glorious exchange occurred:

41. In a response email, one employee objected to the modified chart, stating that removing Tradebot from the analysis was a falsification of the data.

42. In response to this objection, a Director in the Equities division wrote that "the point of the chart is not to show what's in the pool. The point is to market our capability . . . to monitor individual participants in the pool."

43. A Vice President responsible for selling the dark pool to clients disputed that explanation, replying to the group that "[m]y point when selling that picture was always: 'here is a snapshot of the participants in [Barclays' dark pool] as an accurate view of our pool.' I was never using it like an 'illustration'" of Barclays capability to monitor the pool. "I had always liked the idea that we were being transparent, but happy to take liberties if we can all agree" (emphasis added).

44. Barclays' Head of Product Development (who was also the second in command within Barclays' Equities Electronic Trading division) agreed. He responded, "I think the accuracy [of the chart] is secondary to [the] objective" of showing clients that Barclays monitors the trading in its dark pool, and "so if you want to move/kill certain bubbles, it doesn't really matter."

45. Barclays' Head of Equities Sales responded, "Yes! U smart."

The naive reading of that chart is: "We have a lot of institutional investors and very limited predatory trading in our dark pool." But the correct reading of the chart is: "We have software that allows us to produce this chart." The chart is a perfectly self-referential object, demonstrating only that the chart exists. The chart is a chart of how much chart there is.

This is all perfectly clear from the word "Sample." You just have to know how to read it.
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This little story comes, of course, from the complaint in the fraud lawsuit that Schneiderman filed against Barclays yesterday. The thrust of the allegations is that Barclays operated this dark pool, LX, and advertised it to investors by saying that it was a safe space, carefully monitored to be free from predatory high-frequency traders. Because predatory high-frequency traders are Bad, and no institutional investor wants to trade with predatory high-frequency traders.

Meanwhile, Barclays was advertising LX to high-frequency traders by offering them more information, lower fees, and faster connections than it gave to institutional investors. And when those high-frequency traders traded in a way that Barclays's own monitoring flagged as "toxic," Barclays did nothing about it, because it wanted to keep the high-frequency traders happy.

Barclays charges high frequency trading firms little or nothing to trade in its dark pool. For instance, Barclays' charges the two largest participants in its dark pool -- both of which are high frequency trading firms -- virtually nothing to execute trades. Since at least 2011, these firms were charged nothing per share when posting orders, and between $0.0002 and $0.0005 per share when taking available orders.

Let's do some math on that. Barclays's dark pool trades 282 million shares a week, or around 15 billion shares a year. Let's say that 50 percent of that volume came from those two biggest HFTs, that 80 percent of their trading was taking liquidity, and that they paid Barclays $0.0005 per share every time they took liquidity. So those HFTs paid Barclays about $3 million a year.

Barclays made over $4 billion in equities revenue in 2013.
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Why would you rip off your institutional customers who pay you $4 billion, in order to serve your high-frequency trading customers who pay you less than one one-thousandth as much?

Now, to be clear: While it's just a complaint, and Barclays hasn't had a chance to respond, Schneiderman makes a pretty good case that Barclays was deceiving its big institutional customers.
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But this is not quite the same as making a good case that Barclays was ripping off those customers. The complaint is long on evidence of false advertising, but shorter on evidence that the "predatory trading" was actually predatory. There's a certain amount of foamy fulmination at "predatory trading," but nowhere is there any evidence suggesting that Barclays's institutional clients were actually harmed by it.
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Legally, that probably doesn't matter. It's just a complaint, for one thing. And it's a complaint under New York's Martin Act, which says that everything is fraud. Schneiderman doesn't have to prove that Barclays allowed predatory trading in its dark pool. He's just saying that Barclays allowed trading that Barclays itself characterized as predatory, in its own marketing materials. Like Barclays's chart, this lawsuit is a self-referential object.

But if you want to understand what happened here, that revenue breakdown seems like a useful starting point. Barclays's institutional customers paid it a ton of money; its high-frequency trading customers paid it "virtually nothing." But Barclays made its dark pool welcoming to the HFTs, while telling institutions that it was doing the opposite. There's no evidence, yet, that those institutions were harmed, but there is evidence that they were deceived. Why?

Here's a theory. Barclays's pitch, in its way, is not so different from Schneiderman's. It goes like this: You can trade stocks without interacting with professional traders who expect to make money in the short term by interacting with institutional order flow. You can have a market that is just institutions trading with institutions, with no short-term profit-seekers hanging around taking their share.

This is the dream of many institutional investors, and it's the story that every dark pool wants to tell. It's also the story that Schneiderman wants to tell: that HFTs are purely predatory, and that "real" investors would be happy to buy and sell without them.

But there's a problem, which is that it doesn't work very well. When you just put institutional investors in a pool that excludes high-frequency traders, they have a hard time trading with each other. There's not, it turns out, all that much natural liquidity. Which makes sense. Institutional investors with similar goals and time horizons tend to move together. Many strategies are similar, and many institutions don't even have strategies. Index funds and ETFs are an increasing share of the equity market, and they all buy the same stocks at the same time when money flows into equities. If they're just trading with each other, who is selling?

The way to get trading is to put people with different viewpoints, different goals, and different time horizons together in a single pool. High-frequency traders, who make money by providing liquidity rather than by picking stocks that will go up in the long term, interact usefully with real-money investors. And, yes: They make money doing it. You can call this "predatory" if you want.

Barclays, like other dark pool operators, knew this:
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that you can run a pristine dark pool without "predatory" high frequency traders, and without much trading, or you can run a useful dark pool with high-frequency traders. Barclays could have kept its investor clients "safe" from high-frequency trading, but only at the cost of them not trading much. (And thus: not paying Barclays much!) And if you're sending Barclays an order in the first place, it's because you want to trade. You'd probably rather trade with someone who's not making money off of you, instead of with someone who is, but you'd rather trade with someone who is making money than with no one.

But Barclays couldn't just say this, because the reputation of high-frequency trading is so bad. It needed a whole song and dance about how it kept out the bad kinds of high-frequency trading. So that chart says (or, you know, doesn't say): There's no one here who will (1) trade with your order and (2) make money doing it.
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Obviously if you're trying to buy or sell stock, you want someone to trade with your order. Obviously making money is a good reason to trade with an order. But no one can say that. So instead, there are fake charts.

The promise of Barclays LX is the promise of Eric Schneiderman: We can protect you from professional traders who expect to make money trading with you.
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But Barclays couldn't. And Schneiderman probably can't either.

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What is the chart trying to say? Well, first of all, "ELP" means "electronic liquidity provider," that is, high-frequency trader. The circles each represent a trader, with the size of the circles representing the amount of volume each participant trades. The two axes are:

"1 second alpha," meaning the likelihood that prices move up (down) in the second after the trader buys (sells) -- a measure of short-term profitability; and

"modified take percentage," meaning the frequency with which the trader is taking liquidity rather than providing it with a resting order.

You'd expect a "predatory" trader to be profitable in the second after it trades; you wouldn't necessarily expect that from an institution with a long time horizon. The "modified take percentage" strikes me as less of an indication of "predatory" versus non-predatory behavior; plenty of high-frequency traders make plenty of money as market makers, providing rather than taking liquidity. And in fact the green circles (HFTs) in this chart mostly provide liquidity, while the institutions are all over the place, with many posting passive limit orders and many others mostly taking liquidity. But Barclays shades the high-alpha/high-take quadrant pink.

I joked on Twitter, "No one tell Eric Schneiderman how banks construct league tables." The point of a league table is not to provide objective truth about how much M&A or underwriting your bank does. The point of a league table is to produce a nicely formatted chart with your bank's name at the top of it. If it's Martin Act fraud for a bank to puff up its capabilities, then I probably don't want to finish this sentence.

That's 2,672 million pounds in "Equities and Prime Services" (page 261 of the annual report), converted into $4.2 billion at a 1.564 GBPUSD rate that Bloomberg FA seems to use to convert 2013 data.

Or at least trying to, which is all that matters under the Martin Act. The complaint is rich with stories of this deception, and I won't try to point out all of them. Among the most damning is the story of a trading analysis that Barclays prepared for a big institutional client, showing that most of the orders that the investor was sending to Barclays were routed to Barclays's own dark pool.

In preparation for a meeting with the Institutional Investor to explain these findings, two senior Directors prepared a PowerPoint presentation that included the results of the trading analysis. Two days before the scheduled meeting, one of those Directors was called into a meeting with senior leadership in the Equities Electronic Trading division, who instructed him not to disclose the findings to the client. According to this Director, "[t]here was no suggestion at that meeting, or at any other point, that the analysis was wrong," merely that it should not be shared with the client because it reflected poorly on Barclays. Despite the pressure from senior leadership, this Director declined to withhold the findings from Institutional Investor. The next day, and prior to the scheduled meeting with the Institutional Investor, this Director was fired.

This obviously comes from the disgruntled fired guy, so probably take it with a grain of salt. But if it's true, it's not great.

A representative passage:

As described by one former senior-level Director within the Equities Electronics Trading division, "Barclays was doing deals left and right with high frequency firms to invite them into the pool to be trading partners for the buy side. So the pool is mainly made up of high frequency firms." "[T]he way the deal would work is [Barclays] would invite the high frequency firms in. They would trade with the buy side. The buy side would pay the commissions. The high frequency firms would pay basically nothing. They would make their money off of manipulating the price. Barclays would make their money off the buy side. And the buy side would totally be taken advantage of because they got stuck with the bad trade . . . this happened over and over again."

A lot of rhetoric here ("senior-level Director," "left and right," "manipulating the price"), but no explanation for how the high frequency firms could "make their money off of manipulating the price."

For instance, Pipeline. Pipeline was a dark pool that "described its trading platform as a 'crossing network' that matched customer orders with those from other customers, providing 'natural liquidity.' " But, as the Securities and Exchange Commission found in 2011, that wasn't true. Most of those orders were actually secretly matched with a high-frequency trading firm owned by Pipeline:

Pipeline's claims were false and misleading because its parent company owned a trading entity that filled the vast majority of customer orders on Pipeline's system, the SEC found. It said the affiliate, most recently known as Milstream Strategy Group LLC, sought to predict the trading intentions of Pipeline's customers and trade elsewhere in the same direction as customers before filling their orders on Pipeline's platform. The SEC's order found that Pipeline generally did not provide the "natural liquidity" it advertised.

IEX knows this too. IEX, the dark pool that is the hero of Michael Lewis's "Flash Boys," and that is advertised as the "Investors' Exchange," allows some high-frequency traders, though it slows them down to try to prevent latency arbitrage. Because without high-frequency traders, IEX wouldn't trade much stock.

The exception that everyone cites is Liquidnet, which, despite occasional hiccups, really does seem to be a dark pool that is for natural crossing by big investors. This is reflected in its statistics: Its average trade size is much higher than that of most other big dark pools. But it's relatively small, because there's not that much natural crossing. Its volume traded is less than one-tenth as many shares as Barclays LX.

That's an exaggeration, but the pink region is for traders who take liquidity (that is, hit institutional resting bids or lift offers) and make money in the subsequent second.

Part of the selling point of dark pools is that by keeping orders to transact securities private, they are less likely to be prowled by speed traders looking to beat investors who are slower to react to new information. Barclays, according to Schneiderman, sought further to soothe money managers by saying high-frequency firms were policed on its platform. Allegations that they weren't could cause mutual funds and other big investors to wonder if any corner of the market is safe.

Matt Levine is a Bloomberg View columnist. He was an editor of Dealbreaker, an investment banker at Goldman Sachs, a mergers and acquisitions lawyer at Wachtell, Lipton, Rosen & Katz and a clerk for the U.S. Court of Appeals for the Third Circuit.